One of the main goals of near-field scanning microwave microscopy is to quantitatively measure a material's complex microwave permittivity (dielectric constant and conductivity) with a high sensitivity of lateral and/or depth selectivity (i.e. to determine the material's property over a small volume while ignoring the contribution of that volume's surrounding environment). This is particularly important in measurements on complex structures, such as semiconductor devices or composite materials, where, for example, the permittivity of one line or layer must be determined without having knowledge of the properties of the neighboring lines or underlying layers.
In microwave microscopy a basic measurement is a determination of the reflection of a microwave signal from a probe positioned in close proximity to a sample. Phase and amplitude of the reflected signal may be determined directly by using a vector network analyzer or by determination of the resonant frequency and quality factor of a resonator coupled to the probe.
In many cases, the phase of the reflected signal correlates to a large extent with the real part of the sample permittivity, whereas magnitude is dominated by the imaginary part of the permittivity (i.e., the microwave absorption of the sample). Measurements of the microwave transmission from the probe through the sample are also possible, however, such an arrangement generally does not yield a localized determination of a sample's complex permittivity.
The most typical approaches in microwave microscopy employ a coaxial probe geometry also referred to as apertureless probes, in which a central inner conductor (usually an STM tip) protrudes from one end of the probe and is tapered, as shown in FIG. 1. An alternative to the rotationally-symmetric arrangement of the coaxial probes are planar structures such as a co-planar wave-guide or a strip-line wave-guide. The tapered tip is used for concentrating the electric field around and/or underneath the tip apex which permits the probes to ‘image’ features on the order of the tip apex curvature or less. This ‘imaging’ resolution however, is not a quantitative measurement since the probe is averaging over a volume that is usually a few orders of magnitude larger (usually a few millimeters) than the tip apex curvature. While the field concentration around the tip apex is significant, there are also fields that extend over much larger distances. Such an apparatus yields an imaging resolution on the order of the diameter or radius of curvature of the central conductor tip.
It is obvious from considerations of classic electrodynamics that the volume of space over which an apparatus determines the electrical properties of a sample is determined not by the local dimensions of the central conductor tip alone, but rather by a length scale given by the separation between the central conductor tip and the ground (outer) conductor or shield, as shown in FIG. 1.
Therefore, in order to quantitatively determine the microwave properties of a material these properties must be devoid of non-uniformities on length scales of at least several times larger than the distance between the probe tip and the ground conductor while sufficient imaging contrast on length scales comparable to the radius of curvature of the tip may be achieved.
It is further obvious from considerations of classical electrodynamics that the separation between the probe and a sample affects the capacitance measured which is a function of the probe-sample separation and the electrical field distribution. Thus, it is important that the separation between the probe and the sample be measured in order to determine complex permittivity in a non-contact manner. Without accurate control of distance and a small volume of electrical field distribution high lateral and/or depth selectivity and accurate quantitative results cannot be achieved with conventional technology.
Furthermore, the inherent unbalanced character of the exposed portion of the probe complicates the above-mentioned geometries due to the dipole-like current-flow in the surrounding area. The amount of radiation is critically dependent on the environment, i.e., the sample's complex permittivity and the probe-to-sample distance which affects the amplitude of the reflected signal (reflection measurement) or quality factor of the resonator (resonant technique). The result is a potentially erroneous determination of the sample's microwave absorption.
Conventional near-field microwave probes cannot be used for simultaneous near-field optical measurements and complex permittivity measurements due to the fact that the tapered fiber tip serves as a circular waveguide disadvantageously having a cut-off frequency for the optical and microwave radiation.